AS Daily A Level Physics question
Two identical low-friction carts start from rest on a straight track. Cart X is pulled with a constant horizontal force for twice as long as cart Y is pulled with twice that force. The pulls stop at those moments. Which statement must be true?
Answer
The correct answer is B.
Correct: B — They finish with the same speed, and cart X has travelled twice the distance of cart Y. With equal mass, acceleration is proportional to the applied force; X experiences a for twice as long, Y experiences 2a for half as long, so the change in speed (acceleration × time) is the same, but distance from rest depends on acceleration × time^2, making X’s distance twice Y’s. A is wrong because equal final speeds do not guarantee equal distances when the durations of acceleration differ. B is correct as explained. C is wrong because the larger force on Y acts for half the time, giving the same final speed as X, and the distances are not equal. D is wrong because Y does not finish faster; the longer push on X makes X travel farther.